Stickelberger series and Main Conjecture for function fields

Let F be a global function field of characteristic p with ring of integers A and let Φ be a Hayes module on the Hilbert class field H_A of F. We prove an Iwasawa Main Conjecture for the (Z_p)^∞-extension mathcal{F}/F generated by the mathfrak{p}-power torsion of Φ (mathfrak{p} a prime of A). The main tool is a Stickelberger series whose specialization provides a generator for the Fitting ideal of the class group of F. Moreover we prove that the same series, evaluated at complex or mathfrak{p}-adic characters, interpolates the Goss Zeta-function or some mathfrak{p}-adic L-function, thus providing the link between the algebraic structure (class groups) and the analytic functions, which is the crucial part of Iwasawa Main Conjecture

Stickelberger series and Main Conjecture for function fields

Let F be a global function field of characteristic p with ring of integers A and let \Phi be a Hayes module on the Hilbert class field H(A) of F. We prove an Iwasawa Main Conjecture for the Z_p^\infty-extension F/F generated by the \mathfrak{p}-power torsion of \Phi (\mathfrak{p} a prime of A). The main tool is a Stickelberger series whose specialization provides a generator for the Fitting ideal of the class group of F. Moreover we prove that the same series, evaluated at complex or p-adic characters, interpolates the Goss Zeta-function or some p-adic L-function, thus providing the link between the algebraic structure (class groups) and the analytic functions, which is the crucial part of Iwasawa Main Conjecture.Comment: to appear in Publicacions Matem\`atique

Stickelberger series and Main Conjecture for function fields

Let F be a global function field of characteristic p with ring of integers A and let Φ be a Hayes module on the Hilbert class field HA of F. We prove an Iwasawa Main Conjecture for the Z∞p extension F/F generated by the p-power torsion of Φ (p a prime of A). The main tool is a Stickelberger series whose specialization provides a generator for the Fitting ideal of the class group of F. Moreover we prove that the same series, evaluated at complex or p-adic characters, interpolates the Goss Zeta-function or some p-adic L-function, thus providing the link between the algebraic structure (class groups) and the analytic functions, which is the crucial part of Iwasawa Main Conjecture

Absence of neutralizing antibodies against the Omicron SARS-CoV-2 variant in convalescent sera from individuals infected with the ancestral SARS-CoV-2 virus or its Gamma variant

Objectives: The aim of the present study was to evaluate if neutralizing antibody responses induced by infection with the SARS-CoV-2 strain that was dominant at the beginning of the pandemic or by the Gamma variant was effective against the Omicron variant. Methods: Convalescent sera from 109 individuals, never exposed to a SARS-CoV-2 vaccine, who had mild or moderate symptoms not requiring hospitalization following either a documented SARS-CoV-2 ancestral strain infection or a Gamma variant infection, were assayed for in vitro neutralizing antibody activity against their original strains and the Omicron variant. Results: Following an infection with the ancestral strain, 56 (93.3%), 45 (77.6%) and 1 (1.7%) serum sample were positive for neutralizing antibodies against the ancestral, Gamma variant, and Omicron variant, respectively. After infection with the Gamma variant, 43 (87.8%) and 2 (4.1%) sera were positive for neutralizing antibodies against the Gamma and Omicron variants, respectively. Conclusions: Neutralizing antibodies generated following mild or moderate infection with the SARS-CoV-2 ancestral strain or the Gamma variant are not protective against the Omicron variant

Entry of New Drugs and Doctor's Prescriptions

This paper is about entry of new drugs in pharmaceutical markets. More specifically, I analyze the diffusion of new drugs among doctors. My empirical analysis uses non-parametric duration models, which are flexible enough to identify enough to identify the most important covariates influencing the doctors' adoption decisions. My results speak to issues such as why generic drugs do not have large market shares in post-patent drug markets. When I analyze entry of bio-equivalent products, I find that the doctors' past dispersion across drugs in a therapeutic market is the best predictor of the likelihood of adoption. When a new presentation form is introduced by an incumbent firm, the doctors who extensively prescribed the brand in the other presentation forms are the ones most likely to adopt the new drug. Finally, I find that doctors are nor firm-loyal in their prescribing behavior across therapeutic markets

Fitting ideals of class groups in Carlitz-Hayes cyclotomic extensions

We generalize some results of Greither and Popescu to a geometric Galois cover X → Y which appears naturally for example in extensions generated by pn-torsion points of a rank 1 normalized Drinfeld module (i.e. in subextensions of Carlitz-Hayes cyclotomic extensions of global fields of positive characteristic). We obtain a description of the Fitting ideal of class groups (or of their dual) via a formula involving Stickelberger elements and providing a link (similar to the one in [1]) with Goss ζ-function